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arXiv · 1510.09011

A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes

David A. Kopriva·Andrew R. Winters·Marvin Bohm·Gregor J. Gassner
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Abstract

We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free-stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results.

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David A. Kopriva, Andrew R. Winters, Marvin Bohm, Gregor J. Gassner. 2015-10-30. A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes. https://arxiv.org/abs/1510.09011

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